Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 5 cos 3θ

Answer 1

Graph the function, the axis of symmetry is in the x-axis

Answer 2

First of all get a picture of what this looks like. Desmos is a pretty good graphing program, but anything that will do polar coordinates will work. 

Here is the graph.

What you can see is that this graph is symmetrical around the x axis.

When you talk about symmetry, you can think of it as taking a mirror and putting it where you think there is symmetry. If you can't tell the difference between the image and the real thing, then you have symmetry.

In this case, the mirror will show symmetry along the x axis and no where else.